6 ms·

I'll just chime in with my completely ignorant theory that 1 - 0.999... = the infinitely smallest number, but is still, in my mind, regardless of any logic, rea

I'll just chime in with my completely ignorant theory that 1 - 0.999... = the infinitely smallest number, but is still, in my mind, regardless of any logic, reason, or educated calculations, greater than 0. I understand and accept this is wrong. However, somewhere in my brain I still believe it. Sort of like +0 and -0, which are also different in my head.

thdrdt 7y ago
Philosophically you are right. Mathematically you are wrong. It is indeed true that if there was an entity that could reason beyond infinity 1-0.999... would be greater than 0.
- saagarjha 7y ago
  From the perspective of IEEE-754, they’re pretty close ;)
- cthalupa 7y ago
  >It is indeed true that if there was an entity that could reason beyond infinity 1-0.999... would be greater than 0. This seems like a common thread in the comments on this article, and I don't quite understand it. Humans can reason about infinity just fine. We have a hard time picturing it, but it's overall a pretty simple concept: It never ends. So there's no such thing as being able to reason "beyond infinity", because beyond infinity doesn't exist. Its very existence is precluded by the definition of infinity.
Scarblac 7y ago
So 0 and that number are two different numbers. What is the difference between them?
- russellbeattie 7y ago
  One is positive and the other is negative. I thought that was pretty obvious!
mywittyname 7y ago
Well, if you perform the same calculation in base12, then you'll get a whole number representation, because 12 / 3 is 4. Thus, in base 12, 1 / 3 = 0.4 The problem here is our language for mathematics. Just like you have to accept the silent "k" on the word "knife", even when it doesn't make sense, in math, you have to understand that rational numbers can't always be expressed accurately as decimals.
- russellbeattie 7y ago
  Just to be clear, as I said, I totally accept the correct answer. I was just trying to humorously point out the non-intuitive nature of it.

thdrdt 7y ago

Philosophically you are right. Mathematically you are wrong. It is indeed true that if there was an entity that could reason beyond infinity 1-0.999... would be greater than 0.

saagarjha 7y ago
From the perspective of IEEE-754, they’re pretty close ;)
cthalupa 7y ago
>It is indeed true that if there was an entity that could reason beyond infinity 1-0.999... would be greater than 0. This seems like a common thread in the comments on this article, and I don't quite understand it. Humans can reason about infinity just fine. We have a hard time picturing it, but it's overall a pretty simple concept: It never ends. So there's no such thing as being able to reason "beyond infinity", because beyond infinity doesn't exist. Its very existence is precluded by the definition of infinity.

Scarblac 7y ago

So 0 and that number are two different numbers. What is the difference between them?

russellbeattie 7y ago
One is positive and the other is negative. I thought that was pretty obvious!

mywittyname 7y ago

Well, if you perform the same calculation in base12, then you'll get a whole number representation, because 12 / 3 is 4. Thus, in base 12, 1 / 3 = 0.4 The problem here is our language for mathematics. Just like you have to accept the silent "k" on the word "knife", even when it doesn't make sense, in math, you have to understand that rational numbers can't always be expressed accurately as decimals.

russellbeattie 7y ago
Just to be clear, as I said, I totally accept the correct answer. I was just trying to humorously point out the non-intuitive nature of it.